A uniqueness result for a class of singular 𝑝-Laplacian Dirichlet problem with non-monotone forcing term

2021 ◽  
Author(s):  
P. Cong ◽  
D. Hai ◽  
R. Shivaji
Keyword(s):  
Dirichlet Problem ◽  
Uniqueness Result ◽  
Forcing Term

The Dirichlet problem for elliptic equations in weighted Sobolev spaces on unbounded domains of the plane

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Serena Boccia ◽  
Maria Salvato ◽  
Maria Transirico
Keyword(s):  
Dirichlet Problem ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Weighted Sobolev Spaces ◽  
Unbounded Domains ◽  
Uniqueness Result ◽  
Order Linear ◽  
A Priori Bound

AbstractThis paper deals with the Dirichlet problem for second order linear elliptic equations in unbounded domains of the plane in weighted Sobolev spaces. We prove an a priori bound and an existence and uniqueness result.

Uniqueness Result in the Cauchy Dirichlet Problem via Mehler Kernel

2014 ◽  
Vol 53 (9) ◽  
pp. 3046-3051
Author(s):  
Bishnu P. Dhungana
Keyword(s):  
Dirichlet Problem ◽  
Uniqueness Result ◽  
Mehler Kernel

scholarly journals On unique solvability of a Dirichlet problem with nonlinearity depending on the derivative

2019 ◽  
Vol 39 (2) ◽  
pp. 131-144
Author(s):  
Michał Bełdziński ◽  
Marek Galewski
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Unique Solvability ◽  
Existence And Uniqueness ◽  
Variational Approach ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order

In this work we consider second order Dirichelet boundary value problem with nonlinearity depending on the derivative. Using a global diffeomorphism theorem we propose a new variational approach leading to the existence and uniqueness result for such problems.

Solvability of one nonlocal Dirichlet problem for the Poisson equation

2019 ◽  
Vol 50 (1) ◽  
pp. 67-88
Author(s):  
Batirkhan Turmetov ◽  
Valery Karachik
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
The Poisson Equation

scholarly journals Existence of strong solutions to the Dirichlet problem for the Griffith energy

2019 ◽  
Vol 58 (4) ◽  
Author(s):  
Antonin Chambolle ◽  
Vito Crismale
Keyword(s):  
Dirichlet Problem ◽  
Strong Solutions

scholarly journals Note on a sign-dependent regularity for the polyharmonic Dirichlet problem

2021 ◽  
Vol 279 ◽  
pp. 1-9
Author(s):  
Inka Schnieders ◽  
Guido Sweers
Keyword(s):  
Dirichlet Problem

scholarly journals A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian

2021 ◽  
Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Singular Term ◽  
Type Theorem ◽  
Solution Map ◽  
Continuity Properties ◽  
Variational Tools ◽  
Superlinear Reaction

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

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